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of 35
pro vyhledávání: '"Chatzakos, Dimitrios"'
We investigate the mean value of the inner product of squared $\mathrm{GL}_{n}$ degenerate maximal parabolic Eisenstein series against a smooth compactly supported function lying in a restricted space of incomplete Eisenstein series induced from a $\
Externí odkaz:
http://arxiv.org/abs/2311.14184
Publikováno v:
Int. Math. Res. Not. 2024, no. 20, 13180-13190
We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\u{\i}-Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced re
Externí odkaz:
http://arxiv.org/abs/2309.04186
We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane $\mathbb{H}$. The angles of lattice points arising from the orbit of the modular group $PSL_{2}(\mathbb{Z})$, and lying on hyperbolic circles, are sho
Externí odkaz:
http://arxiv.org/abs/2009.10546
We study a refinement of the quantum unique ergodicity conjecture for shrinking balls on arithmetic hyperbolic manifolds, with a focus on dimensions $ 2 $ and $ 3 $. For the Eisenstein series for the modular surface $\mathrm{PSL}_2( {\mathbb Z}) \bac
Externí odkaz:
http://arxiv.org/abs/2007.11473
Akademický článek
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The remainder $E_\Gamma(X)$ in the Prime Geodesic Theorem for the Picard group $\Gamma = \mathrm{PSL}(2,\mathbb{Z}[i])$ is known to be bounded by $O(X^{3/2+\epsilon})$ under the assumption of the Lindel\"of hypothesis for quadratic Dirichlet $L$-func
Externí odkaz:
http://arxiv.org/abs/1812.11916
Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Hee
Externí odkaz:
http://arxiv.org/abs/1808.01318
Autor:
Balkanova, Olga, Chatzakos, Dimitrios, Cherubini, Giacomo, Frolenkov, Dmitry, Laaksonen, Niko
For $\Gamma$ a cofinite Kleinian group acting on $\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\Gamma \backslash \mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics) on $M$. L
Externí odkaz:
http://arxiv.org/abs/1712.00880
Autor:
Chatzakos, Dimitrios
For $\Gamma$ a Fuchsian group of finite covolume, we study the lattice point problem in conjugacy classes on the Riemann surface $\Gamma \backslash \mathbb{H}$. Let $\mathcal{H}$ be a hyperbolic conjugacy class in $\Gamma$ and $\ell$ the $\mathcal{H}
Externí odkaz:
http://arxiv.org/abs/1610.01462
Autor:
Chatzakos, Dimitrios
For $\Gamma$ a cocompact or cofinite Fuchsian group, we study the lattice point problem on the Riemann surface $\Gamma\backslash\mathbb{H}$. The main asymptotic for the counting of the orbit $\Gamma z$ inside a circle of radius $r$ centered at $z$ gr
Externí odkaz:
http://arxiv.org/abs/1512.04137